aerobic digestion tank volume for waste activated sludge stabilization Given influent sludge flow (Q_i) = 233.0 m^3/day; influent volatile solids (X_i) = 19,940 mg/L; BOD fraction factor (F) = 0.5900; influent BOD5 (S_i) = 370.0 mg/L; digester volatile solids (X_d) = 13,420 mg/L; reaction rate constant (K_d) = 0.1420 1/day; volatile fraction (P_v) = 0.6900; digester detention time (theta_c) = 32.5000 day, determine the digester volume (V_d) in m^3.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except V_d is given, so isolate V_d symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for V_d:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

3. Step 3 — List the givens: influent sludge flow (Q_i) = 233.0 m^3/day, influent volatile solids (X_i) = 19,940 mg/L, BOD fraction factor (F) = 0.5900, influent BOD5 (S_i) = 370.0 mg/L, digester volatile solids (X_d) = 13,420 mg/L, reaction rate constant (K_d) = 0.1420 1/day, volatile fraction (P_v) = 0.6900, digester detention time (theta_c) = 32.5000 day.

4. Step 4 — Substitute the given values:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

5. Step 5 — Evaluate:

   V_{d} = 2718\ \text{m^3}

6. Step 6 — Check: returning V_d = 2,718 m^3 to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 5,437 — kept a factor of two that cancels in the correct rearrangement.
• 1,359 — dropped that same factor in the other direction.
• 2,990 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion design of a sludge digester Given influent volatile solids (X_i) = 12,510 mg/L; BOD fraction factor (F) = 0.6300; influent BOD5 (S_i) = 770.0 mg/L; digester volatile solids (X_d) = 9,310 mg/L; reaction rate constant (K_d) = 0.1380 1/day; volatile fraction (P_v) = 0.6300; digester detention time (theta_c) = 20.0000 day; digester volume (V_d) = 13,299 m^3, determine the influent sludge flow (Q_i) in m^3/day.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except Q_i is given, so isolate Q_i symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for Q_i:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

3. Step 3 — List the givens: influent volatile solids (X_i) = 12,510 mg/L, BOD fraction factor (F) = 0.6300, influent BOD5 (S_i) = 770.0 mg/L, digester volatile solids (X_d) = 9,310 mg/L, reaction rate constant (K_d) = 0.1380 1/day, volatile fraction (P_v) = 0.6300, digester detention time (theta_c) = 20.0000 day, digester volume (V_d) = 13,299 m^3.

4. Step 4 — Substitute the given values:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

5. Step 5 — Evaluate:

   Q_{i} = 1305\ \text{m^3/day}

6. Step 6 — Check: returning Q_i = 1,305 m^3/day to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 2,609 — kept a factor of two that cancels in the correct rearrangement.
• 652.4 — dropped that same factor in the other direction.
• 1,435 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion volatile solids reduction sizing calculation Given influent sludge flow (Q_i) = 166.0 m^3/day; influent volatile solids (X_i) = 7,690 mg/L; BOD fraction factor (F) = 0.7400; influent BOD5 (S_i) = 280.0 mg/L; digester volatile solids (X_d) = 15,310 mg/L; reaction rate constant (K_d) = 0.1510 1/day; volatile fraction (P_v) = 0.7200; digester detention time (theta_c) = 25.5000 day, determine the digester volume (V_d) in m^3.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except V_d is given, so isolate V_d symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for V_d:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

3. Step 3 — List the givens: influent sludge flow (Q_i) = 166.0 m^3/day, influent volatile solids (X_i) = 7,690 mg/L, BOD fraction factor (F) = 0.7400, influent BOD5 (S_i) = 280.0 mg/L, digester volatile solids (X_d) = 15,310 mg/L, reaction rate constant (K_d) = 0.1510 1/day, volatile fraction (P_v) = 0.7200, digester detention time (theta_c) = 25.5000 day.

4. Step 4 — Substitute the given values:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

5. Step 5 — Evaluate:

   V_{d} = 578.8\ \text{m^3}

6. Step 6 — Check: returning V_d = 578.8 m^3 to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 1,158 — kept a factor of two that cancels in the correct rearrangement.
• 289.4 — dropped that same factor in the other direction.
• 636.7 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion tank volume for waste activated sludge stabilization Given influent volatile solids (X_i) = 6,490 mg/L; BOD fraction factor (F) = 0.5300; influent BOD5 (S_i) = 2,720 mg/L; digester volatile solids (X_d) = 17,010 mg/L; reaction rate constant (K_d) = 0.1600 1/day; volatile fraction (P_v) = 0.7400; digester detention time (theta_c) = 30.5000 day; digester volume (V_d) = 18,442 m^3, determine the influent sludge flow (Q_i) in m^3/day.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except Q_i is given, so isolate Q_i symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for Q_i:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

3. Step 3 — List the givens: influent volatile solids (X_i) = 6,490 mg/L, BOD fraction factor (F) = 0.5300, influent BOD5 (S_i) = 2,720 mg/L, digester volatile solids (X_d) = 17,010 mg/L, reaction rate constant (K_d) = 0.1600 1/day, volatile fraction (P_v) = 0.7400, digester detention time (theta_c) = 30.5000 day, digester volume (V_d) = 18,442 m^3.

4. Step 4 — Substitute the given values:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

5. Step 5 — Evaluate:

   Q_{i} = 5980\ \text{m^3/day}

6. Step 6 — Check: returning Q_i = 5,980 m^3/day to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 11,959 — kept a factor of two that cancels in the correct rearrangement.
• 2,990 — dropped that same factor in the other direction.
• 6,577 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion design of a sludge digester Given influent sludge flow (Q_i) = 417.0 m^3/day; influent volatile solids (X_i) = 12,560 mg/L; BOD fraction factor (F) = 0.7700; influent BOD5 (S_i) = 310.0 mg/L; digester volatile solids (X_d) = 14,060 mg/L; reaction rate constant (K_d) = 0.1710 1/day; volatile fraction (P_v) = 0.8500; digester detention time (theta_c) = 23.0000 day, determine the digester volume (V_d) in m^3.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except V_d is given, so isolate V_d symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for V_d:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

3. Step 3 — List the givens: influent sludge flow (Q_i) = 417.0 m^3/day, influent volatile solids (X_i) = 12,560 mg/L, BOD fraction factor (F) = 0.7700, influent BOD5 (S_i) = 310.0 mg/L, digester volatile solids (X_d) = 14,060 mg/L, reaction rate constant (K_d) = 0.1710 1/day, volatile fraction (P_v) = 0.8500, digester detention time (theta_c) = 23.0000 day.

4. Step 4 — Substitute the given values:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

5. Step 5 — Evaluate:

   V_{d} = 2010\ \text{m^3}

6. Step 6 — Check: returning V_d = 2,010 m^3 to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 4,020 — kept a factor of two that cancels in the correct rearrangement.
• 1,005 — dropped that same factor in the other direction.
• 2,211 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion volatile solids reduction sizing calculation Given influent volatile solids (X_i) = 3,450 mg/L; BOD fraction factor (F) = 0.6900; influent BOD5 (S_i) = 970.0 mg/L; digester volatile solids (X_d) = 15,360 mg/L; reaction rate constant (K_d) = 0.0990 1/day; volatile fraction (P_v) = 0.7400; digester detention time (theta_c) = 36.5000 day; digester volume (V_d) = 15,919 m^3, determine the influent sludge flow (Q_i) in m^3/day.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except Q_i is given, so isolate Q_i symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for Q_i:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

3. Step 3 — List the givens: influent volatile solids (X_i) = 3,450 mg/L, BOD fraction factor (F) = 0.6900, influent BOD5 (S_i) = 970.0 mg/L, digester volatile solids (X_d) = 15,360 mg/L, reaction rate constant (K_d) = 0.0990 1/day, volatile fraction (P_v) = 0.7400, digester detention time (theta_c) = 36.5000 day, digester volume (V_d) = 15,919 m^3.

4. Step 4 — Substitute the given values:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

5. Step 5 — Evaluate:

   Q_{i} = 5975\ \text{m^3/day}

6. Step 6 — Check: returning Q_i = 5,975 m^3/day to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 11,950 — kept a factor of two that cancels in the correct rearrangement.
• 2,987 — dropped that same factor in the other direction.
• 6,572 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion tank volume for waste activated sludge stabilization Given influent sludge flow (Q_i) = 217.0 m^3/day; influent volatile solids (X_i) = 17,050 mg/L; BOD fraction factor (F) = 0.5500; influent BOD5 (S_i) = 1,540 mg/L; digester volatile solids (X_d) = 8,400 mg/L; reaction rate constant (K_d) = 0.1830 1/day; volatile fraction (P_v) = 0.6800; digester detention time (theta_c) = 26.5000 day, determine the digester volume (V_d) in m^3.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except V_d is given, so isolate V_d symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for V_d:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

3. Step 3 — List the givens: influent sludge flow (Q_i) = 217.0 m^3/day, influent volatile solids (X_i) = 17,050 mg/L, BOD fraction factor (F) = 0.5500, influent BOD5 (S_i) = 1,540 mg/L, digester volatile solids (X_d) = 8,400 mg/L, reaction rate constant (K_d) = 0.1830 1/day, volatile fraction (P_v) = 0.6800, digester detention time (theta_c) = 26.5000 day.

4. Step 4 — Substitute the given values:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

5. Step 5 — Evaluate:

   V_{d} = 2851\ \text{m^3}

6. Step 6 — Check: returning V_d = 2,851 m^3 to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 5,702 — kept a factor of two that cancels in the correct rearrangement.
• 1,425 — dropped that same factor in the other direction.
• 3,136 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion design of a sludge digester Given influent volatile solids (X_i) = 15,160 mg/L; BOD fraction factor (F) = 0.7700; influent BOD5 (S_i) = 810.0 mg/L; digester volatile solids (X_d) = 19,540 mg/L; reaction rate constant (K_d) = 0.0510 1/day; volatile fraction (P_v) = 0.7700; digester detention time (theta_c) = 32.0000 day; digester volume (V_d) = 2,358 m^3, determine the influent sludge flow (Q_i) in m^3/day.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except Q_i is given, so isolate Q_i symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for Q_i:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

3. Step 3 — List the givens: influent volatile solids (X_i) = 15,160 mg/L, BOD fraction factor (F) = 0.7700, influent BOD5 (S_i) = 810.0 mg/L, digester volatile solids (X_d) = 19,540 mg/L, reaction rate constant (K_d) = 0.0510 1/day, volatile fraction (P_v) = 0.7700, digester detention time (theta_c) = 32.0000 day, digester volume (V_d) = 2,358 m^3.

4. Step 4 — Substitute the given values:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

5. Step 5 — Evaluate:

   Q_{i} = 205.9\ \text{m^3/day}

6. Step 6 — Check: returning Q_i = 205.9 m^3/day to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 411.7 — kept a factor of two that cancels in the correct rearrangement.
• 102.9 — dropped that same factor in the other direction.
• 226.4 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion volatile solids reduction sizing calculation Given influent sludge flow (Q_i) = 403.0 m^3/day; influent volatile solids (X_i) = 3,680 mg/L; BOD fraction factor (F) = 0.7400; influent BOD5 (S_i) = 2,970 mg/L; digester volatile solids (X_d) = 17,200 mg/L; reaction rate constant (K_d) = 0.0710 1/day; volatile fraction (P_v) = 0.8300; digester detention time (theta_c) = 40.0000 day, determine the digester volume (V_d) in m^3.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except V_d is given, so isolate V_d symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for V_d:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

3. Step 3 — List the givens: influent sludge flow (Q_i) = 403.0 m^3/day, influent volatile solids (X_i) = 3,680 mg/L, BOD fraction factor (F) = 0.7400, influent BOD5 (S_i) = 2,970 mg/L, digester volatile solids (X_d) = 17,200 mg/L, reaction rate constant (K_d) = 0.0710 1/day, volatile fraction (P_v) = 0.8300, digester detention time (theta_c) = 40.0000 day.

4. Step 4 — Substitute the given values:

   $$V_{d} = \dfrac{Q_i(X_i+FS_i)}{X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}$$

5. Step 5 — Evaluate:

   V_{d} = 1641\ \text{m^3}

6. Step 6 — Check: returning V_d = 1,641 m^3 to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 3,282 — kept a factor of two that cancels in the correct rearrangement.
• 820.4 — dropped that same factor in the other direction.
• 1,805 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion

aerobic digestion tank volume for waste activated sludge stabilization Given influent volatile solids (X_i) = 3,740 mg/L; BOD fraction factor (F) = 0.5600; influent BOD5 (S_i) = 4,460 mg/L; digester volatile solids (X_d) = 17,610 mg/L; reaction rate constant (K_d) = 0.0930 1/day; volatile fraction (P_v) = 0.6800; digester detention time (theta_c) = 16.0000 day; digester volume (V_d) = 13,099 m^3, determine the influent sludge flow (Q_i) in m^3/day.

Start with the thinking

• The governing relation printed in this handbook section is Aerobic Digestion.
• Everything except Q_i is given, so isolate Q_i symbolically first — never rearrange after the numbers are in.
• Tabulate each given with its unit and confirm the units are consistent with the relation before substituting.
• Aerobic digestion sizes the digester volume needed to stabilize waste activated sludge volatile solids.

Step-by-step solution

1. Step 1 — State the governing relation:

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

2. Step 2 — Rearrange symbolically for Q_i:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

3. Step 3 — List the givens: influent volatile solids (X_i) = 3,740 mg/L, BOD fraction factor (F) = 0.5600, influent BOD5 (S_i) = 4,460 mg/L, digester volatile solids (X_d) = 17,610 mg/L, reaction rate constant (K_d) = 0.0930 1/day, volatile fraction (P_v) = 0.6800, digester detention time (theta_c) = 16.0000 day, digester volume (V_d) = 13,099 m^3.

4. Step 4 — Substitute the given values:

   $$Q_{i} = \dfrac{V_d X_d\left(K_dP_v+\dfrac{1}{\theta_c}\right)}{X_i+FS_i}$$

5. Step 5 — Evaluate:

   Q_{i} = 4650\ \text{m^3/day}

6. Step 6 — Check: returning Q_i = 4,650 m^3/day to

   $$V_d = \dfrac{Q_i (X_i + F S_i)}{X_d (K_d P_v + 1/\theta_c)}$$

   reproduces the given quantities, and both sides carry the same units.

Why the other options are there

• 9,300 — kept a factor of two that cancels in the correct rearrangement.
• 2,325 — dropped that same factor in the other direction.
• 5,115 — rounded an intermediate value before the final step.

Reference: FE Handbook — Aerobic Digestion